in a certain algebra 2 class of 22 students, 13 of them play basketball and 10 of them play baseball. there…

in a certain algebra 2 class of 22 students, 13 of them play basketball and 10 of them play baseball. there are 8 students who play both sports. what is the probability that a student chosen randomly from the class plays basketball or baseball?

in a certain algebra 2 class of 22 students, 13 of them play basketball and 10 of them play baseball. there are 8 students who play both sports. what is the probability that a student chosen randomly from the class plays basketball or baseball?

Answer

Explanation:

Step1: Use the formula for $P(A\cup B)$

The formula for the probability of the union of two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, let event $A$ be playing basketball and event $B$ be playing baseball. The total number of students $n = 22$. So $P(A)=\frac{13}{22}$, $P(B)=\frac{10}{22}$ and $P(A\cap B)=\frac{8}{22}$.

Step2: Substitute the values into the formula

$P(A\cup B)=\frac{13}{22}+\frac{10}{22}-\frac{8}{22}=\frac{13 + 10-8}{22}$.

Step3: Calculate the numerator

$13+10 - 8=15$.

Step4: Get the probability

$P(A\cup B)=\frac{15}{22}$.

Answer:

$\frac{15}{22}$